What is the easiest way of figuring out these math problems? It's on a practice PSAT test, and I have no idea.

Question

**I don't want the answer though, because the answers are in the back of my practice packet; I just want to know, how would you approach these problems?**

8) If t + u + v = 42 and 2u + 2v = 60, what is the value of t?
...(A) 12
...(B) 14
...(C) 18
...(D) 24
...(E) 27

16) If (x + y)^2 - (x - y)^2 = 84 and x and y are positive integers, which of the folowing could be the value of x + y?
...(A) 10
...(B) 12
...(C) 14
...(D) 16
...(E) 18

17) In the xy-plane, the line y = ax + 5 is parallel to othe line 3x + 8y = 10. What is the value of a?
...(A) -6
...(B) -8/3
...(C) -3/8
...(D) 3/8
...(E) 8/3

Umm... I'm sorry, but for #16, how did you get the 4xy?

This is what I have so far on #16...

(x+y)^2 - (x-y)^2 = 84

(x+y)(x+y) - (x-y)(x-y) = 84

x^2 + xy + xy + y^2 - x^2 - xy - xy + y^2 = 84

x^2 + 2xy + y^2 - x^2 - 2xy - y^2 = 84

And I think I made an error...

Answer 1

8)2t=2(t+u+v)-2u+2v
Now divide it by 2 to get the value of t
16)4xy=(x+y)^2-(x-y)^2
Therefore xy=84/4=21
21 has only two positive factors 3 and 7
x+y=3+7=10
OOPS! i have missed the last question
3x+8y=10 may be expressed as
8y= -3x+10
or,y=-3x/8 +10/8
Slope is -3/8
The first line will also have the same slope
a= -3/8

Answer 2

8. 2u+2v = 60, 2(u+v)=60, u+v=60/2=30, so t=42-30=12.

16. use a^2 - b^2 = (a+b)(a-b) formula
(x+y+x-y)(x+y-x+y) =84
(2x)(2y)=84
xy=21, only two integers possible 7 and 3
21 and 1 will not give you correct answer

As the sum and difference is squared, it does not matter which is which.

17. In formula y=ax+5, a represents slop. so the question is actually what is the slop of the lines which is same for both lines. So if you find slop of one line, that is the answer.
3x+8y=10 will give you y= -3/8x+10/8, so the slop is -3/8

Answer 3

8) Multiply the first equation by 2 getting 2t+2u+2v = 84
Now subtract the 2nd equation from this and you have your answer.

16) expand the paretheses.
You will get x^2+2xy +y^2 -(x^2-2xy +y^2) = 4xy =84
so xy = 21
One possibility is x =7 and y =3 making x+y =10

17) y= ax+y has a slope of a
3x+8y =10 rewrites to y = -3x/8 +10/8 so slope = -3/8
Since lines are ||, slopes are same , so a = -3/8

Answer 4

8 - subtracting equations.
t + u + v = 42, 2u+2v= 60. Divide the second equation by two
(u + v = 30 ) and subtract it from the first


16.Not sure. I'd juggle terms and see if I got a new expression that I could work with.

17. Parellel lines must have identical slope. (If lines don't have the same slope, eventually they will intersect ) Juggle the 3x + 8y = 10 equation into y=mx+b form.

Answer 5

the explanation must be distinctive for each individual. -Are you timing your self wisely? -have been you under pressure for the duration of the easily examination? -have been there the different varieties of issues on the different examination? perhaps, no longer feeling gentle? Regardless, there's a explanation why a great form of folk like taking it thrice. in case you're doing so nicely on prepare assessments, it fairly is fairly well worth a retake. when I retook my try I went from a 2010 to a 2150, and that i plan to decide for a third attempt in November. stable success.